## 'data.frame': 1599 obs. of 12 variables:
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 4.60 Min. :0.1200 Min. :0.000 Min. : 0.900
## 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090 1st Qu.: 1.900
## Median : 7.90 Median :0.5200 Median :0.260 Median : 2.200
## Mean : 8.32 Mean :0.5278 Mean :0.271 Mean : 2.539
## 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420 3rd Qu.: 2.600
## Max. :15.90 Max. :1.5800 Max. :1.000 Max. :15.500
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :0.01200 Min. : 1.00 Min. : 6.00
## 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00
## Median :0.07900 Median :14.00 Median : 38.00
## Mean :0.08747 Mean :15.87 Mean : 46.47
## 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00
## Max. :0.61100 Max. :72.00 Max. :289.00
## density pH sulphates alcohol
## Min. :0.9901 Min. :2.740 Min. :0.3300 Min. : 8.40
## 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50
## Median :0.9968 Median :3.310 Median :0.6200 Median :10.20
## Mean :0.9967 Mean :3.311 Mean :0.6581 Mean :10.42
## 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10
## Max. :1.0037 Max. :4.010 Max. :2.0000 Max. :14.90
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.636
## 3rd Qu.:6.000
## Max. :8.000
## fixed.acidity volatile.acidity citric.acid
## fixed.acidity 1.00000000 -0.256130895 0.67170343
## volatile.acidity -0.25613089 1.000000000 -0.55249568
## citric.acid 0.67170343 -0.552495685 1.00000000
## residual.sugar 0.11477672 0.001917882 0.14357716
## chlorides 0.09370519 0.061297772 0.20382291
## free.sulfur.dioxide -0.15379419 -0.010503827 -0.06097813
## total.sulfur.dioxide -0.11318144 0.076470005 0.03553302
## density 0.66804729 0.022026232 0.36494718
## pH -0.68297819 0.234937294 -0.54190414
## sulphates 0.18300566 -0.260986685 0.31277004
## alcohol -0.06166827 -0.202288027 0.10990325
## quality 0.12405165 -0.390557780 0.22637251
## ratio_volatile.acidity -0.61795497 0.897649036 -0.72491130
## residual.sugar chlorides free.sulfur.dioxide
## fixed.acidity 0.114776724 0.093705186 -0.153794193
## volatile.acidity 0.001917882 0.061297772 -0.010503827
## citric.acid 0.143577162 0.203822914 -0.060978129
## residual.sugar 1.000000000 0.055609535 0.187048995
## chlorides 0.055609535 1.000000000 0.005562147
## free.sulfur.dioxide 0.187048995 0.005562147 1.000000000
## total.sulfur.dioxide 0.203027882 0.047400468 0.667666450
## density 0.355283371 0.200632327 -0.021945831
## pH -0.085652422 -0.265026131 0.070377499
## sulphates 0.005527121 0.371260481 0.051657572
## alcohol 0.042075437 -0.221140545 -0.069408354
## quality 0.013731637 -0.128906560 -0.050656057
## ratio_volatile.acidity -0.048915832 -0.008546520 0.043217407
## total.sulfur.dioxide density pH
## fixed.acidity -0.11318144 0.66804729 -0.68297819
## volatile.acidity 0.07647000 0.02202623 0.23493729
## citric.acid 0.03553302 0.36494718 -0.54190414
## residual.sugar 0.20302788 0.35528337 -0.08565242
## chlorides 0.04740047 0.20063233 -0.26502613
## free.sulfur.dioxide 0.66766645 -0.02194583 0.07037750
## total.sulfur.dioxide 1.00000000 0.07126948 -0.06649456
## density 0.07126948 1.00000000 -0.34169933
## pH -0.06649456 -0.34169933 1.00000000
## sulphates 0.04294684 0.14850641 -0.19664760
## alcohol -0.20565394 -0.49617977 0.20563251
## quality -0.18510029 -0.17491923 -0.05773139
## ratio_volatile.acidity 0.08260807 -0.27834445 0.51275106
## sulphates alcohol quality
## fixed.acidity 0.183005664 -0.06166827 0.12405165
## volatile.acidity -0.260986685 -0.20228803 -0.39055778
## citric.acid 0.312770044 0.10990325 0.22637251
## residual.sugar 0.005527121 0.04207544 0.01373164
## chlorides 0.371260481 -0.22114054 -0.12890656
## free.sulfur.dioxide 0.051657572 -0.06940835 -0.05065606
## total.sulfur.dioxide 0.042946836 -0.20565394 -0.18510029
## density 0.148506412 -0.49617977 -0.17491923
## pH -0.196647602 0.20563251 -0.05773139
## sulphates 1.000000000 0.09359475 0.25139708
## alcohol 0.093594750 1.00000000 0.47616632
## quality 0.251397079 0.47616632 1.00000000
## ratio_volatile.acidity -0.277126392 -0.09587272 -0.34692938
## ratio_volatile.acidity
## fixed.acidity -0.61795497
## volatile.acidity 0.89764904
## citric.acid -0.72491130
## residual.sugar -0.04891583
## chlorides -0.00854652
## free.sulfur.dioxide 0.04321741
## total.sulfur.dioxide 0.08260807
## density -0.27834445
## pH 0.51275106
## sulphates -0.27712639
## alcohol -0.09587272
## quality -0.34692938
## ratio_volatile.acidity 1.00000000
#分别计算质量与酒精和固定酸度的相关系数
cor.test(wq$quality, wq$alcohol)
##
## Pearson's product-moment correlation
##
## data: wq$quality and wq$alcohol
## t = 21.639, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4373540 0.5132081
## sample estimates:
## cor
## 0.4761663
cor.test(wq$quality, wq$fixed.acidity)
##
## Pearson's product-moment correlation
##
## data: wq$quality and wq$fixed.acidity
## t = 4.996, df = 1597, p-value = 6.496e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.07548957 0.17202667
## sample estimates:
## cor
## 0.1240516
##
## Calls:
## m1: lm(formula = I(quality) ~ I(alcohol), data = wq)
## m2: lm(formula = I(quality) ~ I(alcohol) + alcohol, data = wq)
## m3: lm(formula = I(quality) ~ I(alcohol) + alcohol + volatile.acidity,
## data = wq)
## m4: lm(formula = I(quality) ~ I(alcohol) + alcohol + volatile.acidity +
## citric.acid, data = wq)
## m5: lm(formula = I(quality) ~ I(alcohol) + alcohol + volatile.acidity +
## citric.acid + sulphates, data = wq)
## m6: lm(formula = I(quality) ~ I(alcohol) + alcohol + volatile.acidity +
## citric.acid + fixed.acidity, data = wq)
##
## ==================================================================================================
## m1 m2 m3 m4 m5 m6
## --------------------------------------------------------------------------------------------------
## (Intercept) 1.875*** 1.875*** 3.095*** 3.055*** 2.646*** 2.622***
## (0.175) (0.175) (0.184) (0.194) (0.201) (0.219)
## I(alcohol) 0.361*** 0.361*** 0.314*** 0.314*** 0.309*** 0.325***
## (0.017) (0.017) (0.016) (0.016) (0.016) (0.016)
## volatile.acidity -1.384*** -1.343*** -1.265*** -1.420***
## (0.095) (0.114) (0.113) (0.115)
## citric.acid 0.068 -0.079 -0.314*
## (0.103) (0.104) (0.137)
## sulphates 0.696***
## (0.103)
## fixed.acidity 0.056***
## (0.013)
## --------------------------------------------------------------------------------------------------
## R-squared 0.227 0.227 0.317 0.317 0.336 0.325
## N 1599 1599 1599 1599 1599 1599
## ==================================================================================================
## Significance: *** = p < 0.001; ** = p < 0.01; * = p < 0.05
cor.test(wq$quality, wq$ratio_volatile.acidity) #计算质量与挥发性酸度比率
##
## Pearson's product-moment correlation
##
## data: wq$quality and wq$ratio_volatile.acidity
## t = -14.782, df = 1597, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.3893292 -0.3030624
## sample estimates:
## cor
## -0.3469294